Active billiards: Engineering boundaries for the spatial control of confined active particles

Unlike gas molecules at equilibrium, the spatial organization of self-propelled particles can be very sensitive to what happens at the boundaries of their container. Understanding the link between boundary phenomena and bulk stationary distributions could enable the design of optimized container shapes for the geometric control of confined active particles. Here, we propose a boundary method based on the flux transfer formalism typical of radiometry problems, where surface elements transmit and receive "rays" of active particles with infinite persistence length. We demonstrate the power of this boundary method in the case of the swimming microalgae <i>Euglena gracilis</i> trapped in light-defined billiard geometries. Quite surprisingly, we found that <i>Euglena</i> scatters with a nearly Lambertian cosine law, resembling the behavior of blackbody radiation and consequently resulting in nearly uniform distributions inside simple cavity geometries. Nevertheless, leveraging our boundary method, we were able to design a stacked multistage billiard geometry, with a connection scheme between subunits that breaks spatial symmetry and achieves an exponential amplification of cell concentration between its two ends. Our method can be applied to confined active matter in contexts ranging from spatial control and sorting of microorganisms to the design of efficient navigation strategies for microscopic and macroscopic robots.